Accuracy Calculator

Understanding Classification Accuracy and Confusion Matrix Metrics

Classification accuracy is one of the fundamental evaluation metrics in machine learning, statistics, and medical diagnostic testing. It measures the proportion of correctly predicted outcomes relative to the total number of evaluation samples.

Accuracy Formula

Accuracy is derived directly from the confusion matrix values:

$$\text{Accuracy} = \frac{\text{TP} + \text{TN}}{\text{TP} + \text{TN} + \text{FP} + \text{FN}}$$

Where:

• TP (True Positives): Positive instances correctly identified.
• TN (True Negatives): Negative instances correctly identified.
• FP (False Positives): Negative instances incorrectly flagged as positive (Type I error).
• FN (False Negatives): Positive instances incorrectly flagged as negative (Type II error).

Additional Evaluation Metrics

While accuracy provides a quick high-level summary, it can be misleading on imbalanced datasets. Additional metrics provide a more complete assessment:

• Precision (Positive Predictive Value): $$\text{Precision} = \frac{\text{TP}}{\text{TP} + \text{FP}}$$
• Recall (Sensitivity / True Positive Rate): $$\text{Recall} = \frac{\text{TP}}{\text{TP} + \text{FN}}$$
• Specificity (True Negative Rate): $$\text{Specificity} = \frac{\text{TN}}{\text{TN} + \text{FP}}$$
• F1 Score: Harmonic mean of precision and recall: $$\text{F1} = 2 \times \frac{\text{Precision} \times \text{Recall}}{\text{Precision} + \text{Recall}}$$
• Error Rate: $$\text{Error Rate} = \frac{\text{FP} + \text{FN}}{\text{Total}}$$

For further statistical analysis, explore our Probability Calculator and ANOVA Calculator.